Research | Aslihan Demirkaya
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Aslihan Demirkaya, PhD

My work has been in the analysis of equations: the Kuramoto-Sivashinsky (KS) equation, Burger-Sivashinsky (BS) equation, Klein-Gordon KG type equations, Schrödinger equations, Beam equations and the Spruce-Budworm equation.


  • Demirkaya, M. Stanislavova, Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation, to appear in Journal Discrete and Continuous Dynamical System-B.

  • Hala Al-Khalil, C. Brennan, R. Decker, A. Demirkaya, J. Nagode, Numerical Existence and Stability of Steady State Solutions to the Distributed Spruce Budworm Model, Involve: A Journal of Mathematics, Vol. 10 (2017), No. 5, 857—879

  • A. Demirkaya, S. Hakkaev, On the spectral stability of periodic waves of the coupled Schrödinger equations, Physics Letters A, Vol 379 (2015), Issues 45-46, 2908-2914

  • A. Demirkaya, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, Spectral stability analysis for standing waves of a perturbed Klein-Gordon equation, Dynamical Systems, Differential Equations and Applications AIMS Proceedings, (2015), 359-368

  • A. Demirkaya, S. Hakkaev, M. Stanislavova, A. Stefanov, On the spectral stability of periodic waves of the Klein-Gordon equation,Differential  and Integral Equations, Vol 28 (2015), 431-454

  • A. Demirkaya, T. Kapitula, P.G. Kevrekidis, M. Stanislavova, A. Stefanov, On the spectral stability of kinks in some PT-symmetric variants of the classical Klein-Gordon Field Theories, Studies in Applied Mathematics, Vol. 133, Issue 3, pp.298-317, 2014

  • M. Aron, P. Bowers, N. Byer, R. Decker, A. Demirkaya,Jun Hwan Ryu, Numerical Results using Spectral Methods on Existence and Stability of Steady State Solutions for the Reaction Diffusion and Klein-Gordon Equations, Involve: A Journal of Mathematics, Vol. 7, No. 6, pp.723-742, 2014

  • A. Demirkaya, D. J. Frantzeskakis, P. G. Kevrekidis, A. Saxena, A. Stefanov, Effects of PT -symmetry in Nonlinear Klein-Gordon Field Theories and Their Solitary Waves, Phys. Rev. E 88, 023203, 2013

  • A. Demirkaya, M. Stanislavova, Conditional stability theorem for the one dimensional Klein-Gordon equation, J. Math. Phys. 52, 112703, 2011.

  • A. Demirkaya, M. Stanislavova, Long Time Behavior for Radially Symmetric Solutions of Kuramoto-Sivashinsky Equation in Dimension 3, Dynamics of PDE, Vol.7, No. 2, pp.161-173, 2010.

  • A. Demirkaya, The Existence of a Global Attractor for a Kuramoto-Sivashinsky type Equation in 2D, Discrete and Continuous Dynamical Systems-A, pp.198-207, 2009.

  • A. Demirkaya, $L_2$ estimates for the Solutions of Burger-Sivashinsky Equation in 1D and 2D, AIPS Conference Proceedings, Vol. 1184, pp.105-112, 2009.

To Appear:

  • Christov, A. Demirkaya, P.G. Kevrekidis, A. Saxena, Kink Dynamics in a Parametric φ6 Model.